The force of interest 8 (t) is a function of time and, at any time t...

 

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The force of interest 8 (t) is a function of time and, at any time t (measured in years), is given by the formula 8 (t) = ( 0.04 +0.005t, 0≤t<6 0.16 0.04, 0.015t, 6 ≤ t < 8 8≤t (i) Derive expressions in terms of t for the accumulated amount at time t of an investment of 1 at time 0. [5 marks] (ii) Calculate the value at time 0 of $100 due at time 8. [2 marks] The force of interest 8 (t) is a function of time and, at any time t (measured in years), is given by the formula 8 (t) = ( 0.04 +0.005t, 0≤t<6 0.16 0.04, 0.015t, 6 ≤ t < 8 8≤t (i) Derive expressions in terms of t for the accumulated amount at time t of an investment of 1 at time 0. [5 marks] (ii) Calculate the value at time 0 of $100 due at time 8. [2 marks]

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